Curvature corrected path sampling system for autonomous driving vehicles

ABSTRACT

According to one embodiment, a system determines a first trajectory (e.g., a reference line) based on map and route information of the ADV. The system determines a maximum curvature for a predetermined distance for the first trajectory. The system determines a sampling decay ratio based on the maximum curvature. The system generates one or more sets of sample points for the first trajectory, where each set of sample points include one or more sample points separated by a lateral distance apart based on the sampling decay ratio. The system generates a second trajectory for the ADV based on the sets of sample points to control the ADV, where the second trajectory nudges to a left or a right of the first trajectory based on the maximum curvature of the first trajectory.

TECHNICAL FIELD

Embodiments of the present disclosure relate generally to operatingautonomous vehicles. More particularly, embodiments of the disclosurerelate to a curvature corrected path sampling system for autonomousdriving vehicles (ADVs).

BACKGROUND

Vehicles operating in an autonomous mode (e.g., driverless) can relieveoccupants, especially the driver, from some driving-relatedresponsibilities. When operating in an autonomous mode, the vehicle cannavigate to various locations using onboard sensors, allowing thevehicle to travel with minimal human interaction or in some caseswithout any passengers.

Motion planning and control are critical operations in autonomousdriving. Particularly, trajectory planning is a critical component in anautonomous driving system. Trajectory planning techniques can rely onreference lines, which are guidance paths, e.g., a center line of aroad, for autonomous driving vehicles, to generate stable trajectories.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure are illustrated by way of example and notlimitation in the figures of the accompanying drawings in which likereferences indicate similar elements.

FIG. 1 is a block diagram illustrating a networked system according toone embodiment.

FIG. 2 is a block diagram illustrating an example of a sensor andcontrol system using by an autonomous vehicle according to oneembodiment.

FIGS. 3A-3B are block diagrams illustrating examples of a perception andplanning system used by an autonomous vehicle according to someembodiments.

FIG. 4A is a block diagram illustrating an example of a planning moduleaccording to one embodiment.

FIG. 4B is a block diagram illustrating an example of a curvature-basedtrajectory module according to one embodiment.

FIG. 5A is a diagram illustrating an example of an autonomous vehicletraveling down a road/lane according to some embodiments.

FIG. 5B is a diagram illustrating an example of an autonomous vehicletraveling down a road/lane according to some embodiments.

FIG. 5C is a diagram illustrating an example of an autonomous vehicletraveling down a road/lane according to some embodiments.

FIG. 6 is a flow diagram illustrating a method according to oneembodiment.

FIG. 7 is a block diagram illustrating a data processing systemaccording to one embodiment.

DETAILED DESCRIPTION

Various embodiments and aspects of the disclosures will be describedwith reference to details discussed below, and the accompanying drawingswill illustrate the various embodiments. The following description anddrawings are illustrative of the disclosure and are not to be construedas limiting the disclosure. Numerous specific details are described toprovide a thorough understanding of various embodiments of the presentdisclosure. However, in certain instances, well-known or conventionaldetails are not described in order to provide a concise discussion ofembodiments of the present disclosures.

Reference in the specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin conjunction with the embodiment can be included in at least oneembodiment of the disclosure. The appearances of the phrase “in oneembodiment” in various places in the specification do not necessarilyall refer to the same embodiment.

Embodiments of the disclosures disclose a curvature-based path samplingsystem to generate a driving trajectory for an ADV. According to oneaspect, a system determines a first trajectory (e.g., a reference line)based on map and route information of the ADV. The system determines amaximum curvature for a predetermined distance for the first trajectory.The system determines a sampling decay ratio based on the maximumcurvature. The system generates one or more sets of sample points forthe first trajectory, where each set of sample points include one ormore sample points separated by a lateral distance apart based on thesampling decay ratio. The system generates a second trajectory for theADV based on the sets of sample points to control the ADV, where thesecond trajectory nudges to a left or a right of the first trajectorybased on the maximum curvature of the first trajectory.

In one embodiment, processing logic further generates a number ofsegments to be connected between the sets of sample points and generatesthe second trajectory for the ADV based on the number of segments. Inone embodiment, processing logic further redistributes each set ofsample points to generate a replacement set by merging sample points inthe set if a distance between any two of the sample points in the set issmaller than a predetermined threshold.

In one embodiment, the predetermined distance for the first trajectoryis calculated based on a current speed of the ADV. In one embodiment,the sampling decay ratio is assigned a first predetermined value ifC_max>C_UB, a second predetermined value if C_max<C_LB, or a value of(C_max−C_LB)/(C_UB−C_LB) otherwise, wherein C_max is the maximumcurvature, CUB is determined based on a turning capability of the ADV torepresent an curvature upper bound, and C_LB is a constant representinga curvature lower bound.

In one embodiment, each sample point of a set is separated a lateraldistance from another sample point of the set, wherein the lateraldistance is proportional to the sampling decay ratio for the set ofsample points. In one embodiment, generating the one or more sets ofsample points includes determining a distance between each of the setsof sample points based on a speed of the ADV.

In one embodiment, generating the number of segments between the sets ofsample points includes connecting each sample point in the set of samplepoints to each sample point in an adjacent set of sample points. Inanother embodiment, generating the number of segments between the setsof sample points includes determining a number of polynomial functionsfor the number of segments, where each polynomial function representsone segment of the number of segments. In another embodiment,coefficients of each polynomial are determined based on one or more of alocation of the ADV, a direction of the ADV, a curvature of the ADV, ora curvature change rate of the ADV associated with a respective segment.In another embodiment, each polynomial function includes a quinticpolynomial function or a cubic polynomial function. In one embodiment,generating the second trajectory for the ADV includes determining aplurality of costs for the plurality of segments, determining the pathbased on the plurality of costs, and generating the second trajectorybased on the path.

FIG. 1 is a block diagram illustrating an autonomous vehicle networkconfiguration according to one embodiment of the disclosure. Referringto FIG. 1, network configuration 100 includes autonomous vehicle 101that may be communicatively coupled to one or more servers 103-104 overa network 102. Although there is one autonomous vehicle shown, multipleautonomous vehicles can be coupled to each other and/or coupled toservers 103-104 over network 102. Network 102 may be any type ofnetworks such as a local area network (LAN), a wide area network (WAN)such as the Internet, a cellular network, a satellite network, or acombination thereof, wired or wireless. Server(s) 103-104 may be anykind of servers or a cluster of servers, such as Web or cloud servers,application servers, backend servers, or a combination thereof. Servers103-104 may be data analytics servers, content servers, trafficinformation servers, map and point of interest (MPOI) severs, orlocation servers, etc.

An autonomous vehicle refers to a vehicle that can be configured to inan autonomous mode in which the vehicle navigates through an environmentwith little or no input from a driver. Such an autonomous vehicle caninclude a sensor system having one or more sensors that are configuredto detect information about the environment in which the vehicleoperates. The vehicle and its associated controller(s) use the detectedinformation to navigate through the environment. Autonomous vehicle 101can operate in a manual mode, a full autonomous mode, or a partialautonomous mode.

In one embodiment, autonomous vehicle 101 includes, but is not limitedto, perception and planning system 110, vehicle control system 111,wireless communication system 112, user interface system 113, and sensorsystem 115. Autonomous vehicle 101 may further include certain commoncomponents included in ordinary vehicles, such as, an engine, wheels,steering wheel, transmission, etc., which may be controlled by vehiclecontrol system 111 and/or perception and planning system 110 using avariety of communication signals and/or commands, such as, for example,acceleration signals or commands, deceleration signals or commands,steering signals or commands, braking signals or commands, etc.

Components 110-115 may be communicatively coupled to each other via aninterconnect, a bus, a network, or a combination thereof. For example,components 110-115 may be communicatively coupled to each other via acontroller area network (CAN) bus. A CAN bus is a vehicle communicationstandard designed to allow microcontrollers and devices to communicatewith each other in applications without a host computer. It is amessage-based protocol, designed originally for multiplex electricalwiring within automobiles, but is also used in many other contexts.

Referring now to FIG. 2, in one embodiment, sensor system 115 includes,but it is not limited to, one or more cameras 211, global positioningsystem (GPS) unit 212, inertial measurement unit (IMU) 213, radar unit214, and a light detection and range (LIDAR) unit 215. GPS system 212may include a transceiver operable to provide information regarding theposition of the autonomous vehicle. IMU unit 213 may sense position andorientation changes of the autonomous vehicle based on inertialacceleration. Radar unit 214 may represent a system that utilizes radiosignals to sense objects within the local environment of the autonomousvehicle. In some embodiments, in addition to sensing objects, radar unit214 may additionally sense the speed and/or heading of the objects.LIDAR unit 215 may sense objects in the environment in which theautonomous vehicle is located using lasers. LIDAR unit 215 could includeone or more laser sources, a laser scanner, and one or more detectors,among other system components. Cameras 211 may include one or moredevices to capture images of the environment surrounding the autonomousvehicle. Cameras 211 may be stationary cameras and/or PTZ(pan-tilt-zoom) cameras. A camera may be mechanically movable, forexample, by mounting the camera on a rotating and/or tilting a platform.

Sensor system 115 may further include other sensors, such as, a sonarsensor, an infrared sensor, a steering sensor, a throttle sensor, abraking sensor, and an audio sensor (e.g., microphone). An audio sensormay be configured to capture sound from the environment surrounding theautonomous vehicle. A steering sensor (e.g., electric power steering(EPS)) may be configured to sense the steering angle of a steeringwheel, wheels of the vehicle, or a combination thereof. A throttlesensor and a braking sensor sense the throttle position and brakingposition of the vehicle, respectively. In some situations, a throttlesensor and a braking sensor may be integrated as an integratedthrottle/braking sensor.

Vehicle control system 111 can include, but is not limited to, steeringunit 201, throttle unit 202 (also referred to as an acceleration unit),and braking unit 203. Steering unit 201 is to adjust the direction orheading of the vehicle. Throttle unit 202 is to control the speed of themotor or engine that in turn controls the speed and acceleration of thevehicle. Braking unit 203 is to decelerate the vehicle by providingfriction to slow the wheels or tires of the vehicle. Note that thecomponents as shown in FIG. 2 may be implemented in hardware, software,or a combination thereof

Referring back to FIG. 1, wireless communication system 112 is to allowcommunication between autonomous vehicle 101 and external systems, suchas devices, sensors, other vehicles, etc. For example, wirelesscommunication system 112 can wirelessly communicate with one or moredevices directly or via a communication network, such as servers 103-104over network 102. Wireless communication system 112 can use any cellularcommunication network or a wireless local area network (WLAN), e.g.,using WiFi to communicate with another component or system. Wirelesscommunication system 112 could communicate directly with a device (e.g.,a mobile device of a passenger, a display device, a speaker withinvehicle 101), for example, using an infrared link, Bluetooth, etc. Userinterface system 113 may be part of peripheral devices implementedwithin vehicle 101 including, for example, a keyword, a touch screendisplay device, a microphone, and a speaker, etc.

Some or all of the functions of autonomous vehicle 101 may be controlledor managed by perception and planning system 110, especially whenoperating in an autonomous driving mode. Perception and planning system110 includes the necessary hardware (e.g., processor(s), memory,storage) and software (e.g., operating system, planning and routingprograms) to receive information from sensor system 115, control system111, wireless communication system 112, and/or user interface system113, process the received information, plan a route or path from astarting point to a destination point, and then drive vehicle 101 basedon the planning and control information. Alternatively, perception andplanning system 110 may be integrated with vehicle control system 111.

For example, a user as a passenger may specify a starting location and adestination of a trip, for example, via a user interface. Perception andplanning system 110 obtains the trip related data. For example,perception and planning system 110 may obtain location and routeinformation from an MPOI server, which may be a part of servers 103-104.The location server provides location services and the MPOI serverprovides map services and the POIs of certain locations. Alternatively,such location and MPOI information may be cached locally in a persistentstorage device of perception and planning system 110.

While autonomous vehicle 101 is moving along the route, perception andplanning system 110 may also obtain real-time traffic information from atraffic information system or server (TIS). Note that servers 103-104may be operated by a third party entity. Alternatively, thefunctionalities of servers 103-104 may be integrated with perception andplanning system 110. Based on the real-time traffic information, MPOIinformation, and location information, as well as real-time localenvironment data detected or sensed by sensor system 115 (e.g.,obstacles, objects, nearby vehicles), perception and planning system 110can plan an optimal route and drive vehicle 101, for example, viacontrol system 111, according to the planned route to reach thespecified destination safely and efficiently.

Server 103 may be a data analytics system to perform data analyticsservices for a variety of clients. In one embodiment, data analyticssystem 103 includes data collector 121 and machine learning engine 122.Data collector 121 collects driving statistics 123 from a variety ofvehicles, either autonomous vehicles or regular vehicles driven by humandrivers. Driving statistics 123 include information indicating thedriving commands (e.g., throttle, brake, steering commands) issued andresponses of the vehicles (e.g., speeds, accelerations, decelerations,directions) captured by sensors of the vehicles at different points intime. Driving statistics 123 may further include information describingthe driving environments at different points in time, such as, forexample, routes (including starting and destination locations), MPOIs,road conditions, weather conditions, etc.

Based on driving statistics 123, machine learning engine 122 generatesor trains a set of rules, algorithms, and/or models 124 for a variety ofpurposes. In one embodiment, for example, algorithms/models 124 mayinclude one or more algorithms or models to determine a sampling decayratio for the purposes of lateral sampling points for planning a path toautonomous drive a vehicle. The algorithms/models 124 can be uploadedonto ADVs to be used for autonomous driving by the ADVs, in real-time.

FIGS. 3A and 3B are block diagrams illustrating an example of aperception and planning system used with an autonomous vehicle accordingto one embodiment. System 300 may be implemented as a part of autonomousvehicle 101 of FIG. 1 including, but is not limited to, perception andplanning system 110, control system 111, and sensor system 115.Referring to FIGS. 3A-3B, perception and planning system 110 includes,but is not limited to, localization module 301, perception module 302,prediction module 303, decision module 304, planning module 305, controlmodule 306, routing/sampling module 307, and curvature-based trajectorymodule 308.

Some or all of modules 301-308 may be implemented in software, hardware,or a combination thereof. For example, these modules may be installed inpersistent storage device 352, loaded into memory 351, and executed byone or more processors (not shown). Note that some or all of thesemodules may be communicatively coupled to or integrated with some or allmodules of vehicle control system 111 of FIG. 2. Some of modules 301-308may be integrated together as an integrated module. For example,curvature-based trajectory module 308 and planning module 305 may beintegrated as a single module.

Localization module 301 determines a current location of autonomousvehicle 300 (e.g., leveraging GPS unit 212) and manages any data relatedto a trip or route of a user. Localization module 301 (also referred toas a map and route module) manages any data related to a trip or routeof a user. A user may log in and specify a starting location and adestination of a trip, for example, via a user interface. Localizationmodule 301 communicates with other components of autonomous vehicle 300,such as map and route information 311, to obtain the trip related data.For example, localization module 301 may obtain location and routeinformation from a location server and a map and POI (MPOI) server. Alocation server provides location services and an MPOI server providesmap services and the POIs of certain locations, which may be cached aspart of map and route information 311. While autonomous vehicle 300 ismoving along the route, localization module 301 may also obtainreal-time traffic information from a traffic information system orserver.

Based on the sensor data provided by sensor system 115 and localizationinformation obtained by localization module 301, a perception of thesurrounding environment is determined by perception module 302. Theperception information may represent what an ordinary driver wouldperceive surrounding a vehicle in which the driver is driving. Theperception can include the lane configuration (e.g., straight or curvelanes), traffic light signals, a relative position of another vehicle, apedestrian, a building, crosswalk, or other traffic related signs (e.g.,stop signs, yield signs), etc., for example, in a form of an object. Thelane configuration includes information describing a lane or lanes, suchas, for example, a shape of the lane (e.g., straight or curvature), awidth of the lane, how many lanes in a road, one-way or two-way lane,merging or splitting lanes, exiting lane, etc.

Perception module 302 may include a computer vision system orfunctionalities of a computer vision system to process and analyzeimages captured by one or more cameras in order to identify objectsand/or features in the environment of autonomous vehicle. The objectscan include traffic signals, road way boundaries, other vehicles,pedestrians, and/or obstacles, etc. The computer vision system may usean object recognition algorithm, video tracking, and other computervision techniques. In some embodiments, the computer vision system canmap an environment, track objects, and estimate the speed of objects,etc. Perception module 302 can also detect objects based on othersensors data provided by other sensors such as a radar and/or LIDAR.

For each of the objects, prediction module 303 predicts how the objectwill behave under the circumstances. The prediction is performed basedon the perception data perceiving the driving environment at the pointin time in view of a set of map/route information 311 and traffic rules312. For example, if the object is a vehicle at an opposing directionand the current driving environment includes an intersection, predictionmodule 303 will predict whether the vehicle will likely move straightforward or make a turn. If the perception data indicates that theintersection has no traffic light, prediction module 303 may predictthat the vehicle may have to fully stop prior to enter the intersection.If the perception data indicates that the vehicle is currently at aleft-turn only lane or a right-turn only lane, prediction module 303 maypredict that the vehicle will more likely make a left turn or right turnrespectively.

For each of the objects, decision module 304 makes a decision regardinghow to handle the object. For example, for a particular object (e.g.,another vehicle in a crossing route) as well as its metadata describingthe object (e.g., a speed, direction, turning angle), decision module304 decides how to encounter the object (e.g., overtake, yield, stop,pass). Decision module 304 may make such decisions according to a set ofrules such as traffic rules or driving rules 312, which may be stored inpersistent storage device 352.

Routing module 307 is configured to provide one or more routes or pathsfrom a starting point to a destination point. For a given trip from astart location to a destination location, for example, received from auser, routing module 307 obtains route and map information 311 anddetermines all possible routes or paths from the starting location toreach the destination location. Routing module 307 may generate areference line in a form of a topographic map for each of the routes itdetermines from the starting location to reach the destination location.A reference line refers to an ideal route or path without anyinterference from others such as other vehicles, obstacles, or trafficcondition. That is, if there is no other vehicle, pedestrians, orobstacles on the road, an ADV should exactly or closely follows thereference line. The topographic maps are then provided to decisionmodule 304 and/or planning module 305. Decision module 304 and/orplanning module 305 examine all of the possible routes to select andmodify one of the most optimal route in view of other data provided byother modules such as traffic conditions from localization module 301,driving environment perceived by perception module 302, and trafficcondition predicted by prediction module 303. The actual path or routefor controlling the ADV may be close to or different from the referenceline provided by routing module 307 dependent upon the specific drivingenvironment at the point in time.

Based on a decision for each of the objects perceived, planning module305 plans a path or route for the autonomous vehicle, as well as drivingparameters (e.g., distance, speed, and/or turning angle). That is, for agiven object, decision module 304 decides what to do with the object,while planning module 305 determines how to do it. For example, for agiven object, decision module 304 may decide to pass the object, whileplanning module 305 may determine whether to pass on the left side orright side of the object. Planning and control data is generated byplanning module 305 including information describing how vehicle 300would move in a next moving cycle (e.g., next route/path segment). Forexample, the planning and control data may instruct vehicle 300 to move10 meters at a speed of 30 mile per hour (mph), then change to a rightlane at the speed of 25 mph.

Based on the planning and control data, control module 306 controls anddrives the autonomous vehicle, by sending proper commands or signals tovehicle control system 111, according to a route or path defined by theplanning and control data. The planning and control data includesufficient information to drive the vehicle from a first point to asecond point of a route or path using appropriate vehicle settings ordriving parameters (e.g., throttle, braking, and turning commands) atdifferent points in time along the path or route.

In one embodiment, the planning phase is performed in a number ofplanning cycles, also referred to as command cycles, such as, forexample, in every time interval of 100 milliseconds (ms). For each ofthe planning cycles or command cycles, one or more control commands willbe issued based on the planning and control data. That is, for every 100ms, planning module 305 plans a next route segment or path segment, forexample, including a target position and the time required for the ADVto reach the target position. Alternatively, planning module 305 mayfurther specify the specific speed, direction, and/or steering angle,etc. In one embodiment, planning module 305 plans a route segment orpath segment for the next predetermined period of time such as 5seconds. For each planning cycle, planning module 305 plans a targetposition for the current cycle (e.g., next 5 seconds) based on a targetposition planned in a previous cycle. Control module 306 then generatesone or more control commands (e.g., throttle, brake, steering controlcommands) based on the planning and control data of the current cycle.

Note that decision module 304 and planning module 305 may be integratedas an integrated module. Decision module 304/planning module 305 mayinclude a navigation system or functionalities of a navigation system todetermine a driving path for the autonomous vehicle. For example, thenavigation system may determine a series of speeds and directionalheadings to effect movement of the autonomous vehicle along a path thatsubstantially avoids perceived obstacles while generally advancing theautonomous vehicle along a roadway-based path leading to an ultimatedestination. The destination may be set according to user inputs viauser interface system 113. The navigation system may update the drivingpath dynamically while the autonomous vehicle is in operation. Thenavigation system can incorporate data from a GPS system and one or moremaps so as to determine the driving path for the autonomous vehicle.

Decision module 304/planning module 305 may further include a collisionavoidance system or functionalities of a collision avoidance system toidentify, evaluate, and avoid or otherwise negotiate potential obstaclesin the environment of the autonomous vehicle. For example, the collisionavoidance system may effect changes in the navigation of the autonomousvehicle by operating one or more subsystems in control system 111 toundertake swerving maneuvers, turning maneuvers, braking maneuvers, etc.The collision avoidance system may automatically determine feasibleobstacle avoidance maneuvers on the basis of surrounding trafficpatterns, road conditions, etc. The collision avoidance system may beconfigured such that a swerving maneuver is not undertaken when othersensor systems detect vehicles, construction barriers, etc. in theregion adjacent the autonomous vehicle that would be swerved into. Thecollision avoidance system may automatically select the maneuver that isboth available and maximizes safety of occupants of the autonomousvehicle. The collision avoidance system may select an avoidance maneuverpredicted to cause the least amount of acceleration in a passenger cabinof the autonomous vehicle.

FIG. 4A is a block diagram illustrating an example of a planning module305 according to some embodiments. Referring to FIG. 4A, planning module305 includes, but is not limited to, a segmenter 401, a polynomialfunction generator 402, a sample point generator 403, a path generator404, and a reference line generator 405. These modules 401-405 may beimplemented in software, hardware, or a combination thereof. Referenceline generator 405 is configured to generate a reference line for theADV. As discussed above, the reference line may be a guidance path,e.g., a center line of a road, for the ADV, to generate stabletrajectories. The reference line generator 405 may generate thereference line based on map and route information 311 (illustrated inFIGS. 3A and 3B). Segmenter 401 is configured to segment the referenceline into a number of reference line segments. The reference line may bedivided into reference line segments to generate discrete segments orportions of the reference line. For each of the reference line segments,polynomial function generator 402 may be configured to define andgenerate a polynomial function to represent or model the correspondingreference line segment. The sample point generator 403 may generatesample points based on the reference line, e.g., within close proximity.For example, the sample point generator 403 may generate one or moresets of sample points (e.g., groups of one or more sample points) thatare may generally follow the reference line, as discussed in more detailbelow. Each set of sample points may include a first subset of samplepoints and a second subset of sample points which are staggered from thefirst subset.

The polynomial function generator 402 may connect the multiple sets ofsample points to each other. For example, the polynomial functiongenerator 402 may generate one or more segments (e.g., connections)between each sample point in a set of sample points and each sample inthe next adjacent set of sample points, as discussed in more detailbelow. The polynomial function generator 402 may also generate,calculate, determine, etc., one or more polynomials that may be used torepresent the segments between the sample points. For example, thepolynomial function generator 402 may generate, determine, calculate,etc., a polynomial function for each segment between two sample points.The polynomial functions that represent the segments may also begenerated, determined, calculated based on various boundaries orconstraints. The boundaries or constraints may be preconfigured and/orstored as a part of constraints/algorithms 313 illustrated in FIG. 3A.The polynomial functions used by the planning module 305 (e.g., used bythe polynomial function generator 402) may be preconfigured and/orstored as a part of polynomial functions 314 illustrated in FIG. 3A.

The path generator 404 may determine a path for the ADV based on thesegments between the sample points, as discussed in more detail below.For example, the path generator 404 may determine a cost for eachsegment. The cost may be based on various factors or parametersincluding, but not limited to, how far away the segment is from thereference line, how far away the sample points in the segment are fromthe reference line, the curvature change rate for a segment or forsample points in the segment, the curvature of a segment, obstacles(e.g., a vehicle, a pedestrian, an obstruction, etc.) that may belocated at a sample point, etc. The costs may also be referred to asweights. The path generator 404 may identify or select the segments thatform a path which has the lowest total cost (lowest total weight).

FIG. 4B is a block diagram illustrating an example of a curvature-basedtrajectory module according to one embodiment. Curvature-basedtrajectory module 308 can apply a curvature-based sampling algorithm togenerate a driving trajectory for the ADV. Referring to FIG. 4B,curvature-based trajectory module 308 includes, but is not limited to,trajectory determine/generator 411, max curvature determiner 412,sampling decay ratio determiner 413, and curvature-based sample pointsgenerator 414. These modules 411-414 may be implemented in software,hardware, or a combination thereof. Trajectory determiner/generator 411can determine/generate a driving trajectory based on a reference line.Max curvature determiner 412 can determine a maximum curvature along aportion of a trajectory. Sampling decay ratio determiner 413 candetermine a sampling decay ratio based for a portion of a trajectoryusing the maximum curvature. The algorithm to calculate the samplingdecay ratio may be preconfigured and/or stored as a part ofconstraints/algorithms 313 illustrated in FIG. 3A. Curvature basedsample point generator 414 can generate one or more sample points orsets of samplings point according to a sampling decay ratio for areference line (or trajectory) for the ADV.

FIGS. 5A-5B are diagrams illustrating an example of ADV 101 traveling(e.g., moving, driving, etc.) down road/lane 506 according to someembodiments. Reference line 510 may be generated for ADV 101 using areference line generator. The reference line 510 may be a guidance pathat a center line of road/lane 506 for the ADV 101. In one embodiment, asample point generator may generate sample points 507 (illustrated bythe black dots) to a left or a right lateral distance from referenceline 510. The sample points may be grouped into groups or sets of samplepoints. As illustrated in FIG. 5A, the sample points 507 are groupedinto three sets of sample points, set 520, set 530, and set 540. Each ofthe sets 520, 530, and 540 may be separated by a predetermined distanceapart from each other. In one embodiment, the separation distancebetween adjacent sets is a constant (e.g., 10 meters, 20 meters, or 30meters, etc. apart). In another embodiment, the separation distancebetween adjacent sets is proportional to a current velocity of ADV 101.

Each set of sample points can have one or more sample points. In anotherembodiment, each sample points in a set may be separate by a constantdistance such that the sample points of the set form a lateral lineperpendicular to reference line 510 (e.g., for a width of lane 506). Inanother embodiment, the lateral separation distance is determined basedon a width of a lane of the ADV (e.g., lane 506). The road 506, samplepoints 507, reference line 510, and/or other elements illustrated inFIG. 5 may be represented using a Cartesian coordinate system asillustrated by the X axis and Y-axis in FIG. 5A. For example, thelocation of the ADV 101 may be represented using an X-Y coordinate. Inanother example, a sample point 507 may be represented using astation-lateral (e.g., S-L) coordinate.

Referring to FIG. 5B, in one embodiment, the polynomial functiongenerator 402 may generate polynomials (e.g., line segments) thatconnect the sample points of one set of sample points, to the samplepoints of an adjacent set of sample points. As illustrated by the linesbetween the sample points 507 in sets 520 and 530, the polynomialfunction generator 402 may generate segments that connect each samplepoint in set 520 to each sample point in set 530. For example, thepolynomial function generator 402 may generate twenty-five segments thatconnect the five sample points 507 in set 520, to the five sample points507 in set 530. The polynomial function generator 402 may also generatesegments (e.g., twenty-five additional segments) that connect eachsample point in set 530 to each sample point in set 540, as illustratedby the lines between sample points 507 in sets 530 and 540. In someembodiments, the polynomial function generator 402 may also generate,determine, calculate, etc., polynomial functions (e.g., quintic or cubicpolynomial functions) to represent or model each of the segments usingequations (1) through (12), as discussed above. For example, similar tothe line segments 511 and 512, the polynomial function generator 402 maydetermine a polynomial function and coefficients for the polynomialfunction for each segment (e.g., for each of the fifty segmentsillustrated in FIG. 5B).

In one embodiment, the path generator 404 may determine a path (and atrajectory) for the ADV 101 based on the segments between the samplepoints, as discussed in more detail below. The path generator 404 maydetermine a cost (e.g., a weight) for each of the segments. The cost maybe based on various factors or parameters including, but not limited to,how far away the segment is from the reference line, how far away thesample points in the segment are from the reference line, the curvatureof a segment, the curvature at a sample point, the curvature at astarting point and/or ending point of a segment, the curvature changerate for a segment, the curvature change rate at a sample point, thecurvature change rate at a starting point and/or an endpoint of asegment, obstacles that may be located at a sample point, etc.

In one embodiment, the line segments may be represented using one ormore polynomial functions. For example, the polynomial functiongenerator 402 may generate a polynomial function θ(s) to represent linesegment 511 and a different polynomial function θ(s) to represent linesegment 512 (e.g., the reference line segments 511 and 512 may bemodeled using polynomial functions). In one embodiment, a derivative(e.g., the first order derivative) of the polynomial function representsa curvature along the line segment, K=dθ/ds. A second order derivativeof the polynomial function represents a curvature change or curvaturechange rate, dK/ds, along the line segment.

For the purpose of illustration, following terms are defined:

-   -   θ₀: starting direction    -   {dot over (θ)}₀: starting curvature, k, direction derivative        w.r.t. curve length, i.e.,

$\frac{d\;\theta}{ds}$

-   -   {umlaut over (θ)}₀: starting curvature derivative, i.e.,

$\frac{d_{\kappa}}{ds}$

-   -   θ₁: ending direction    -   {dot over (θ)}₁: ending curvature    -   {umlaut over (θ)}₁: ending curvature derivative    -   Δs: the curve length between the two ends

Each polynomial (or piecewise curve or line segment) may include sevenparameters: starting direction (θ0), starting curvature (dθ0), startingcurvature derivative (d2θ0), ending direction (θ1), ending curvature(dθ1), ending curvature derivative (d2θ1) and the curve length betweenthe starting and ending points (Δs). In one embodiment, the polynomialfunction may be a quintic polynomial function. A quintic polynomialfunction may be defined by equation (1) (e.g., a formula, a function,etc.) as follows:

In another embodiment, the polynomial function may be a cubicpolynomial. A cubic polynomial may be defined by equation (8) asfollows:θ_(i)(s)=a*s ³ +b*s ² +c*s+f   (8)and the cubic polynomial may satisfy the same conditions (indicatedabove with respect to the quintic polynomial function) illustrated byequations (2) through (7).

In one embodiment, to ensure a smooth connection between any two linesegments or polynomial functions, a polynomial function of a linesegment (i) evaluated at an end point should be the same as or similarto a polynomial function of a subsequent line segment (i+1) evaluated ata start point. A first order derivative of the polynomial function ofthe line segment (i) evaluated at the end point should be the same as orsimilar to a first order derivative of the polynomial function of thesubsequent line segment (i+1) evaluated at the start point. A secondorder derivative of the polynomial function of the line segment (i)evaluated at the end point should be the same as or similar to a secondorder derivative of the polynomial function of the line segment (i+1)evaluated at the start point.

For example, for line segment 511 as shown in FIGS. 5A-5B, an output ofthe corresponding polynomial function θ(0) represents a direction orangle of a starting point of line segment 511. Let θ(Δs0) represents adirection of ending point of line segments 511, where the ending pointof line segments 511 is also the starting point of the next line segment512. A first order derivative of θ(0) represents a curvature at thestarting point of line segment 511 and a second order derivative of θ(0)represents a curvature change rate at the ending point of line segment511. A first order derivative of θ(Δs0) represents a curvature of theending point of line segment 511 and a second order derivative of θ(Δs0)represents a curvature change rate of the ending point of line segment511.

By substituting in the above variables, there are six equations that maybe utilized to solve the coefficients of the polynomial function a, b,c, d, e, and f. For example, as stated above, the direction at a givenpoint may be defined using the above quintic polynomial function:θ(s)=as ⁵ +bs ⁴ +cs ³ +ds ² +es+f   (9)

The first order derivative of the quintic polynomial function representsa curvature at the point of the path:dθ=5as ⁴+4bs ³+3cs ²+2ds+e   (10)

The second order derivative of the quintic polynomial functionrepresents a curvature change rate at the point of the path:d ²θ=20as ³+12bs ²+6cs+2d   (11)

For a given line segment, where the direction, curvature, and curvaturechange rate of a starting point and an ending point may be representedby the above three equations respectively. Thus, there are a total ofsix equations for each line segment. These six equations may be utilizedto determine the coefficients a, b, c, d, e, and f of the correspondingquintic polynomial function.

Based on the above constraints, path generator 404 may identify orselect the segments that form a path (e.g., smooth connections) throughmultiple sets of segments which have the lowest total cost (lowest totalweight). For example, trajectory generator 404 can generate a path basedon segments costs using a cost optimization algorithm and/or a dynamicprogramming algorithm, such as Dijkstra's algorithm to select ordetermine a path (and a trajectory) having a lowest total cost. Thetrajectory is then used to control the ADV according to the trajectory.Note that a trajectory has a path and a speed component. The speedcomponent may be a speed limit for road 506 or a speed of a vehicle infront of the ADV for the ADV to follow.

The optimization of the above functions may be performed such that theoverall output of these functions for the different paths reach aminimum, while the above set of constraints are satisfied. In addition,the coordinates of the terminal point derived from the optimization isrequired to be within a predetermined range (e.g., tolerance, errormargins) with respect to the corresponding coordinates of the initialreference line. That is, the difference between each optimized point andthe corresponding point of the initial reference line should be within apredetermined threshold.

FIG. 5C is a diagram illustrating an example of an autonomous vehicletraveling down a road/lane according to some embodiments. The example ofFIG. 5C is similar to the example of FIG. 5B except that acurvature-based sampling algorithm is applied to restrict a lateralsampling of the line segments for trajectory generation for the exampleillustrated in FIG. 5C. Referring to FIG. 5C, in one embodiment, amaximum curvature determiner, such as determiner 412 of FIG. 4B,determines a maximum curvature for reference line 510 for a portion ofreference line 510, e.g., a predetermined distance along reference line510 starting from ADV 101. The distance may be a constant distance or adistance proportional to a current velocity of the ADV. In oneembodiment, the predetermined distance for the maximum curvaturedetermination is eight times the velocity of the ADV. Maximum curvaturedeterminer then determines a maximum curvature for this length ofreference line 510 (the predetermined distance).

Once the maximum curvature is determined, a sampling decay ratiodeterminer, such as determiner 413 of FIG. 4B, determines a samplingdecay ratio for the corresponding length of reference line 510. In oneembodiment, the sampling decay ratio is assigned a first predeterminedvalue (e.g., 0) if C_max>C_UB, a second predetermined value (e.g., 1) ifC_max<C_LB, or a value of (C_max−C_LB)/(C_UB−C_LB) otherwise, whereinC_max is a maximum curvature of reference line 510, C_UB is an upperbound curvature, and C_LB is a lower bound curvature. Here, C_UB may bedetermined based on a turning capability of the ADV (e.g., a valuebetween 0.2 and 0.3) to represent an upper bound of the curvature, andC_LB may be assigned a constant value of 0.01 to represent a lower boundof the curvature. In effect, the determined sampling decay ratio is apositive real value less than or equal to 1.

Curvature-based sampling generator 414 can then generate sets of samplepoints. As discussed above, each set of sample points may be separatedby a constant distance from one another (e.g., sets 550, 560 and 570 canbe situated 10 meters, 20 meters, or 30 meters, etc. apart) or may beseparated by a distance proportional to a speed of the ADV. Within eachset, in one embodiment, the sample points are situated a lateraldistance apart, the lateral distance being proportional to the samplingdecay ratio. For example, sample points 507 for set 560 may be separatedlaterally apart according to the sampling decay ratio (in comparisonwith set 530 of FIG. 5B, the lateral distance from the sample points toline 510 of set 560 is adjusted by the sampling decay ratio). In oneembodiment, as the maximum curvature increases for a portion of road506, the sampling decay ratio decreases. In effect, the nudge-ability ofthe ADV laterally to a left or a right from reference line 510 decreasesas the curvature for road 506 increases.

In another embodiment, a set of sample points may be redistributed.Redistribution can merge two or more sample points within a set ofsample points if a distance between any two of the sample points in theset is smaller than a predetermined threshold. For example, if a lengthof road 506 has a small turning ratio (large curvature), there may be noroom for the ADV to nudge to a left or a right of the reference line510. Referring to FIG. 5C, set 570 may be within a length of road with ahigh maximum curvature. In this case, the sample points for set 570 maybe redistributed. For example, initially, five sample points may begenerated for set 570. However because two points to the left ofreference line are situated so close to each other (e.g., a distanceless than the predetermined threshold), the two points merge into asingle sample point. In one embodiment, merging two sample points mayjoin the two sample points into a single sample point having acoordinate at a midpoint between the two sample points being merged. Inanother embodiment, merging two sample points into a single sample pointincludes eliminating one of the points, such as eliminating a pointfurther away from reference line 510 or a point closest to referenceline 510.

Similarly, the two points to the right of reference line are situated soclose to each other (e.g., less than the predetermined thresholddistance), they merge into a single sample point to the right ofreference line. Thus, only three sample points are available for set 570to make connections with adjacent sets. The reduction or merging ofsample point in effect reduces a computational burden for the ADV asfewer combinations of connections are feasible.

As described above, planning module 305 then connect each sample pointin one set of sample points to a sample point in an adjacent set usingdifferent polynomial function constraints. In addition, a number ofpolynomial functions are used to represent these segments ofconnections, where each polynomial represents one segment. A number ofcosts can be associated for each of the segments. An optimizationalgorithm can then determine a path based on minimization of the costsfor the different segments. Once a path is determined, a trajectory canthen be generated based on the path. Note that a trajectory has a pathand a speed component. The speed component may be a speed limit for road506 or a speed of a vehicle ahead of the ADV 101.

FIG. 6 is a flow diagram illustrating a method according to oneembodiment. Processing 600 may be performed by processing logic whichmay include software, hardware, or a combination thereof. For example,process 600 may be performed by planning module 305 and/orcurvature-based trajectory module 308 of FIG. 3A. Referring to FIG. 6,at block 601, processing logic determines a first trajectory (e.g.,reference line) based on map and route information of the ADV. At block602, processing logic determines a maximum curvature for a predetermineddistance for the first trajectory. At block 603, processing logicdetermines a sampling decay ratio based on the maximum curvature. Atblock 604, processing logic generates one or more sets of sample pointsfor the first trajectory, where each set of sample points includes oneor more sample points separated by a lateral distance apart based on thesampling decay ratio. At block 605, processing logic generates a secondtrajectory (e.g., driving trajectory) for the ADV based on the sets ofsample points to control the ADV, where the second trajectory nudges toa left or a right of the first trajectory based on the maximum curvatureof the first trajectory (e.g., reference line).

In one embodiment, processing logic further generates a number ofsegments to be connected between the sets of sample points and generatesthe second trajectory for the ADV based on the number of segments. Inone embodiment, processing logic further redistributes each set ofsample points to generate a replacement set by merging sample points inthe set if a distance between any two of the sample points in the set issmaller than a predetermined threshold.

In one embodiment, the predetermined distance for the first trajectoryis calculated based on a current speed of the ADV. In one embodiment,the sampling decay ratio is assigned a first predetermined value ifC_max>C_UB, a second predetermined value if C_max<C_LB, or a value of(C_max−C_LB)/(C_UB−C_LB) otherwise, wherein C_max is the maximumcurvature, C_UB is determined based on a turning capability of the ADVto represent an curvature upper bound, and C_LB is a constantrepresenting a curvature lower bound.

In one embodiment, each sample point of a set is separated a lateraldistance from another sample point of the set, wherein the lateraldistance is proportional to the sampling decay ratio for the set ofsample points. In one embodiment, generating the one or more sets ofsample points includes determining a distance between each of the setsof sample points based on a speed of the ADV.

In one embodiment, generating the number of segments between the sets ofsample points includes connecting each sample point in the set of samplepoints to each sample point in an adjacent set of sample points. Inanother embodiment, generating the number of segments between the setsof sample points includes determining a number of polynomial functionsfor the number of segments, where each polynomial function representsone segment of the number of segments. In another embodiment,coefficients of each polynomial are determined based on one or more of alocation of the ADV, a direction of the ADV, a curvature of the ADV, ora curvature change rate of the ADV associated with a respective segment.In another embodiment, each polynomial function includes a quinticpolynomial function or a cubic polynomial function. In one embodiment,generating the second trajectory for the ADV includes determining aplurality of costs for the plurality of segments, determining the pathbased on the plurality of costs, and generating the second trajectorybased on the path.

Note that some or all of the components as shown and described above maybe implemented in software, hardware, or a combination thereof. Forexample, such components can be implemented as software installed andstored in a persistent storage device, which can be loaded and executedin a memory by a processor (not shown) to carry out the processes oroperations described throughout this application. Alternatively, suchcomponents can be implemented as executable code programmed or embeddedinto dedicated hardware such as an integrated circuit (e.g., anapplication specific IC or ASIC), a digital signal processor (DSP), or afield programmable gate array (FPGA), which can be accessed via acorresponding driver and/or operating system from an application.Furthermore, such components can be implemented as specific hardwarelogic in a processor or processor core as part of an instruction setaccessible by a software component via one or more specificinstructions.

FIG. 7 is a block diagram illustrating an example of a data processingsystem which may be used with one embodiment of the disclosure. Forexample, system 1500 may represent any of data processing systemsdescribed above performing any of the processes or methods describedabove, such as, for example, perception and planning system 110 orservers 103-104 of FIG. 1. System 1500 can include many differentcomponents. These components can be implemented as integrated circuits(ICs), portions thereof, discrete electronic devices, or other modulesadapted to a circuit board such as a motherboard or add-in card of thecomputer system, or as components otherwise incorporated within achassis of the computer system.

Note also that system 1500 is intended to show a high level view of manycomponents of the computer system. However, it is to be understood thatadditional components may be present in certain implementations andfurthermore, different arrangement of the components shown may occur inother implementations. System 1500 may represent a desktop, a laptop, atablet, a server, a mobile phone, a media player, a personal digitalassistant (PDA), a Smartwatch, a personal communicator, a gaming device,a network router or hub, a wireless access point (AP) or repeater, aset-top box, or a combination thereof. Further, while only a singlemachine or system is illustrated, the term “machine” or “system” shallalso be taken to include any collection of machines or systems thatindividually or jointly execute a set (or multiple sets) of instructionsto perform any one or more of the methodologies discussed herein.

In one embodiment, system 1500 includes processor 1501, memory 1503, anddevices 1505-1508 connected via a bus or an interconnect 1510. Processor1501 may represent a single processor or multiple processors with asingle processor core or multiple processor cores included therein.Processor 1501 may represent one or more general-purpose processors suchas a microprocessor, a central processing unit (CPU), or the like. Moreparticularly, processor 1501 may be a complex instruction set computing(CISC) microprocessor, reduced instruction set computing (RISC)microprocessor, very long instruction word (VLIW) microprocessor, orprocessor implementing other instruction sets, or processorsimplementing a combination of instruction sets. Processor 1501 may alsobe one or more special-purpose processors such as an applicationspecific integrated circuit (ASIC), a cellular or baseband processor, afield programmable gate array (FPGA), a digital signal processor (DSP),a network processor, a graphics processor, a communications processor, acryptographic processor, a co-processor, an embedded processor, or anyother type of logic capable of processing instructions.

Processor 1501, which may be a low power multi-core processor socketsuch as an ultra-low voltage processor, may act as a main processingunit and central hub for communication with the various components ofthe system. Such processor can be implemented as a system on chip (SoC).Processor 1501 is configured to execute instructions for performing theoperations and steps discussed herein. System 1500 may further include agraphics interface that communicates with optional graphics subsystem1504, which may include a display controller, a graphics processor,and/or a display device.

Processor 1501 may communicate with memory 1503, which in one embodimentcan be implemented via multiple memory devices to provide for a givenamount of system memory. Memory 1503 may include one or more volatilestorage (or memory) devices such as random access memory (RAM), dynamicRAM (DRAM), synchronous DRAM (SDRAM), static RAM (SRAM), or other typesof storage devices. Memory 1503 may store information includingsequences of instructions that are executed by processor 1501, or anyother device. For example, executable code and/or data of a variety ofoperating systems, device drivers, firmware (e.g., input output basicsystem or BIOS), and/or applications can be loaded in memory 1503 andexecuted by processor 1501. An operating system can be any kind ofoperating systems, such as, for example, Robot Operating System (ROS),Windows® operating system from Microsoft®, Mac OS®/iOS® from Apple,Android® from Google®, LINUX, UNIX, or other real-time or embeddedoperating systems.

System 1500 may further include 10 devices such as devices 1505-1508,including network interface device(s) 1505, optional input device(s)1506, and other optional 10 device(s) 1507. Network interface device1505 may include a wireless transceiver and/or a network interface card(NIC). The wireless transceiver may be a WiFi transceiver, an infraredtransceiver, a Bluetooth transceiver, a WiMax transceiver, a wirelesscellular telephony transceiver, a satellite transceiver (e.g., a globalpositioning system (GPS) transceiver), or other radio frequency (RF)transceivers, or a combination thereof. The NIC may be an Ethernet card.

Input device(s) 1506 may include a mouse, a touch pad, a touch sensitivescreen (which may be integrated with display device 1504), a pointerdevice such as a stylus, and/or a keyboard (e.g., physical keyboard or avirtual keyboard displayed as part of a touch sensitive screen). Forexample, input device 1506 may include a touch screen controller coupledto a touch screen. The touch screen and touch screen controller can, forexample, detect contact and movement or break thereof using any of aplurality of touch sensitivity technologies, including but not limitedto capacitive, resistive, infrared, and surface acoustic wavetechnologies, as well as other proximity sensor arrays or other elementsfor determining one or more points of contact with the touch screen.

IO devices 1507 may include an audio device. An audio device may includea speaker and/or a microphone to facilitate voice-enabled functions,such as voice recognition, voice replication, digital recording, and/ortelephony functions. Other IO devices 1507 may further include universalserial bus (USB) port(s), parallel port(s), serial port(s), a printer, anetwork interface, a bus bridge (e.g., a PCI-PCI bridge), sensor(s)(e.g., a motion sensor such as an accelerometer, gyroscope, amagnetometer, a light sensor, compass, a proximity sensor, etc.), or acombination thereof. Devices 1507 may further include an imagingprocessing subsystem (e.g., a camera), which may include an opticalsensor, such as a charged coupled device (CCD) or a complementarymetal-oxide semiconductor (CMOS) optical sensor, utilized to facilitatecamera functions, such as recording photographs and video clips. Certainsensors may be coupled to interconnect 1510 via a sensor hub (notshown), while other devices such as a keyboard or thermal sensor may becontrolled by an embedded controller (not shown), dependent upon thespecific configuration or design of system 1500.

To provide for persistent storage of information such as data,applications, one or more operating systems and so forth, a mass storage(not shown) may also couple to processor 1501. In various embodiments,to enable a thinner and lighter system design as well as to improvesystem responsiveness, this mass storage may be implemented via a solidstate device (SSD). However in other embodiments, the mass storage mayprimarily be implemented using a hard disk drive (HDD) with a smalleramount of SSD storage to act as a SSD cache to enable non-volatilestorage of context state and other such information during power downevents so that a fast power up can occur on re-initiation of systemactivities. Also a flash device may be coupled to processor 1501, e.g.,via a serial peripheral interface (SPI). This flash device may providefor non-volatile storage of system software, including BIOS as well asother firmware of the system.

Storage device 1508 may include computer-accessible storage medium 1509(also known as a machine-readable storage medium or a computer-readablemedium) on which is stored one or more sets of instructions or software(e.g., module, unit, and/or logic 1528) embodying any one or more of themethodologies or functions described herein. Processingmodule/unit/logic 1528 may represent any of the components describedabove, such as, for example, curvature-based trajectory module 308 ofFIG. 3A. Processing module/unit/logic 1528 may also reside, completelyor at least partially, within memory 1503 and/or within processor 1501during execution thereof by data processing system 1500, memory 1503 andprocessor 1501 also constituting machine-accessible storage media.Processing module/unit/logic 1528 may further be transmitted or receivedover a network via network interface device 1505.

Computer-readable storage medium 1509 may also be used to store the somesoftware functionalities described above persistently. Whilecomputer-readable storage medium 1509 is shown in an exemplaryembodiment to be a single medium, the term “computer-readable storagemedium” should be taken to include a single medium or multiple media(e.g., a centralized or distributed database, and/or associated cachesand servers) that store the one or more sets of instructions. The terms“computer-readable storage medium” shall also be taken to include anymedium that is capable of storing or encoding a set of instructions forexecution by the machine and that cause the machine to perform any oneor more of the methodologies of the present disclosure. The term“computer-readable storage medium” shall accordingly be taken toinclude, but not be limited to, solid-state memories, and optical andmagnetic media, or any other non-transitory machine-readable medium.

Processing module/unit/logic 1528, components and other featuresdescribed herein can be implemented as discrete hardware components orintegrated in the functionality of hardware components such as ASICS,FPGAs, DSPs or similar devices. In addition, processingmodule/unit/logic 1528 can be implemented as firmware or functionalcircuitry within hardware devices. Further, processing module/unit/logic1528 can be implemented in any combination hardware devices and softwarecomponents.

Note that while system 1500 is illustrated with various components of adata processing system, it is not intended to represent any particulararchitecture or manner of interconnecting the components; as suchdetails are not germane to embodiments of the present disclosure. Itwill also be appreciated that network computers, handheld computers,mobile phones, servers, and/or other data processing systems which havefewer components or perhaps more components may also be used withembodiments of the disclosure.

Some portions of the preceding detailed descriptions have been presentedin terms of algorithms and symbolic representations of operations ondata bits within a computer memory. These algorithmic descriptions andrepresentations are the ways used by those skilled in the dataprocessing arts to most effectively convey the substance of their workto others skilled in the art. An algorithm is here, and generally,conceived to be a self-consistent sequence of operations leading to adesired result. The operations are those requiring physicalmanipulations of physical quantities.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the above discussion, itis appreciated that throughout the description, discussions utilizingterms such as those set forth in the claims below, refer to the actionand processes of a computer system, or similar electronic computingdevice, that manipulates and transforms data represented as physical(electronic) quantities within the computer system's registers andmemories into other data similarly represented as physical quantitieswithin the computer system memories or registers or other suchinformation storage, transmission or display devices.

Embodiments of the disclosure also relate to an apparatus for performingthe operations herein. Such a computer program is stored in anon-transitory computer readable medium. A machine-readable mediumincludes any mechanism for storing information in a form readable by amachine (e.g., a computer). For example, a machine-readable (e.g.,computer-readable) medium includes a machine (e.g., a computer) readablestorage medium (e.g., read only memory (“ROM”), random access memory(“RAM”), magnetic disk storage media, optical storage media, flashmemory devices).

The processes or methods depicted in the preceding figures may beperformed by processing logic that comprises hardware (e.g. circuitry,dedicated logic, etc.), software (e.g., embodied on a non-transitorycomputer readable medium), or a combination of both. Although theprocesses or methods are described above in terms of some sequentialoperations, it should be appreciated that some of the operationsdescribed may be performed in a different order. Moreover, someoperations may be performed in parallel rather than sequentially.

Embodiments of the present disclosure are not described with referenceto any particular programming language. It will be appreciated that avariety of programming languages may be used to implement the teachingsof embodiments of the disclosure as described herein.

In the foregoing specification, embodiments of the disclosure have beendescribed with reference to specific exemplary embodiments thereof. Itwill be evident that various modifications may be made thereto withoutdeparting from the broader spirit and scope of the disclosure as setforth in the following claims. The specification and drawings are,accordingly, to be regarded in an illustrative sense rather than arestrictive sense.

What is claimed is:
 1. A computer-implemented method to generate a driving trajectory for an autonomous driving vehicle (ADV), the method comprising: in response to a first trajectory generated for the ADV, determining a maximum curvature of the first trajectory; determining a sampling decay ratio based on the maximum curvature; generating one or more sets of sample points based the first trajectory, wherein each set of sample points comprises one or more sample points separated apart by a lateral distance that is determined based on the sampling decay ratio; and generating a second trajectory for the ADV based on the sets of sample points to autonomously drive the ADV.
 2. The method of claim 1, further comprising generating a plurality of segments to be connected between the sets of sample points; and generating the second trajectory for the ADV based on the plurality of segments.
 3. The method of claim 1, further comprising redistributing each set of sample points to generate a replacement set by merging sample points in the set if a distance between any two of the sample points in the set is smaller than a predetermined threshold.
 4. The method of claim 1, wherein a predetermined distance for the first trajectory is calculated based on a current speed of the ADV.
 5. The method of claim 1, wherein the sampling decay ratio is assigned a first predetermined value if C_max>C_UB, a second predetermined value if C_max<C_LB, or a value of (C_max-C_LB)/(C_UB-C_LB) otherwise, wherein C_max is the maximum curvature, CUB is determined based on a turning capability of the ADV to represent an curvature upper bound, and C_LB is a constant representing a curvature lower bound.
 6. The method of claim 1, wherein each sample point of a set is separated a lateral distance from another sample point of the set, wherein the lateral distance is proportional to the sampling decay ratio for the set of sample points.
 7. The method of claim 1, wherein generating the one or more sets of sample points comprises: determining a distance between each of the sets of sample points based on a speed of the ADV.
 8. The method of claim 2, wherein generating the plurality of segments between the sets of sample points comprises: connecting each sample point in the set of sample points to each sample point in an adjacent set of sample points.
 9. The method of claim 8, wherein generating the plurality of segments between the sets of sample points comprises: determining a plurality of polynomial functions for the plurality of segments, wherein each polynomial function represents one segment of the plurality of segments.
 10. The method of claim 9, wherein coefficients of each polynomial are determined based on one or more of a location of the ADV, a direction of the ADV, a curvature of the ADV, or a curvature change rate of the ADV associated with a respective segment.
 11. The method of claim 9, wherein each polynomial function comprises a quintic polynomial function or a cubic polynomial function.
 12. The method of claim 2, wherein generating the second trajectory for the ADV comprises: determining a plurality of costs for the plurality of segments; determining a path based on the plurality of costs; and generating the second trajectory based on the path.
 13. A non-transitory machine-readable medium having instructions stored therein, which when executed by a processor, cause the processor to perform operations of generating a driving trajectory for an autonomous driving vehicle (ADV), the operations comprising: in response to a first trajectory generated for the ADV, determining a maximum curvature of the first trajectory; determining a sampling decay ratio based on the maximum curvature; generating one or more sets of sample points based the first trajectory, wherein each set of sample points comprises one or more sample points separated apart by a lateral distance that is determined based on the sampling decay ratio; and generating a second trajectory for the ADV based on the sets of sample points to autonomously drive the ADV.
 14. The non-transitory machine-readable medium of claim 13, the operations further comprising: generating a plurality of segments to be connected between the sets of sample points; and generating the second trajectory for the ADV based on the plurality of segments.
 15. The non-transitory machine-readable medium of claim 13, the operations further comprising redistributing each set of sample points to generate a replacement set by merging sample points in the set if a distance between any two of the sample points in the set is smaller than a predetermined threshold.
 16. The non-transitory machine-readable medium of claim 13, wherein a predetermined distance for the first trajectory is calculated based on a current speed of the ADV.
 17. The non-transitory machine-readable medium of claim 13, wherein the sampling decay ratio is assigned a first predetermined value if C_max>C_UB, a second predetermined value if C_max<C_LB, or a value of (C_max-C_LB)/(C_UB-C_LB) otherwise, wherein C_max is the maximum curvature, C_UB is determined based on a turning capability of the ADV to represent an curvature upper bound, and C_LB is a constant representing a curvature lower bound.
 18. A data processing system, comprising: a processor; and a memory coupled to the processor to store instructions, which when executed by the processor, cause the processor to perform operations of generating a driving trajectory for an autonomous driving vehicle (ADV), the operations including: in response to a first trajectory generated for the ADV, determining a maximum curvature of the first trajectory, determining a sampling decay ratio based on the maximum curvature, generating one or more sets of sample points based the first trajectory, wherein each set of sample points comprises one or more sample points separated apart by a lateral distance that is determined based on the sampling decay ratio, and generating a second trajectory for the ADV based on the sets of sample points to autonomously drive the ADV.
 19. The system of claim 18, the operations further comprising: generating a plurality of segments to be connected between the sets of sample points; and generating the second trajectory for the ADV based on the plurality of segments.
 20. The system of claim 18, the operations further comprising redistributing each set of sample points to generate a replacement set by merging sample points in the set if a distance between any two of the sample points in the set is smaller than a predetermined threshold.
 21. The system of claim 18, wherein the sampling decay ratio is assigned a first predetermined value if C_max>C_UB, a second predetermined value if C_max<C_LB, or a value of (C_max-C_LB)/(C_UB-C_LB) otherwise, wherein C_max is the maximum curvature, C_UB is determined based on a turning capability of the ADV to represent an curvature upper bound, and C_LB is a constant representing a curvature lower bound. 